In this paper, we investigate synchronization of coupled second-order linear harmonic oscillators with random noises and time delays. The interaction topology is modeled by a weighted directed graph and the weights are perturbed by white noise. On the basis of stability theory of stochastic differential delay equations, algebraic graph theory and matrix theory, we show that the coupled harmonic...

Numerical calculations and analysis of the tension states in hard tissues of tooth are very interesting and important issues from the orthodontist’s point of view. Orthodontic methods of treatment can have a dramatic effect on children’s long-term dental health and facial appearance. Research done in this field shows that due to understanding mechanics of masticatory organ it is possible to att...

The resonance characteristics of vibrating structures change when they are immersed in fluids and these changes can be related to the parameters density viscosity Newtonian liquids. various suitable structures, vibration modes, transduction principles, signal analysis methods lead an immense variety sensor systems reported literature. In this review, we focus on basic similarities between elect...

Abstract. In this paper we point out the existence of a remarkable nonlocal transformation between the damped harmonic oscillator and a modified Emden type nonlinear oscillator equation with linear forcing, ẍ+αxẋ+βx+γx = 0,which preserves the form of the time independent integral, conservative Hamiltonian and the equation of motion. Generalizing this transformation we prove the existence of non...

This paper addresses the amplitude and phase dynamics of a large system of nonlinearly coupled, non-identical damped harmonic oscillators, which is based on recent research in coupled oscillation in optomechanics. Our goal is to investigate the existence and stability of collective behaviour which occurs due to a play-off between the distribution of individual oscillator frequency and the type ...

Abstract. This paper presents sufficient conditions which guarantee that the equilibrium of the damped harmonic oscillator x′′ + h(t)x′ + ωx = 0 is uniformly asymptotically stable, where h : [0,∞) → [0,∞) is locally integrable. These conditions work to suppress the rapid growth of the frictional force expressed by the integral amount of the damping coefficient h. The obtained sufficient conditi...